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Promoting Holistic Problem Solving In Mechanics Pedagogy

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2007 Annual Conference & Exposition


Honolulu, Hawaii

Publication Date

June 24, 2007

Start Date

June 24, 2007

End Date

June 27, 2007



Conference Session

Innovative Teaching Techniques in Mechanics

Tagged Division


Page Count


Page Numbers

12.1206.1 - 12.1206.15



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Paper Authors


Christopher Papadopoulos

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Chris Papadopoulos is Assistant Professor of Civil Engineering and Mechanics at the University of Wisconsin-Milwaukee. He is the PI of the UWM Computer Science, Engineering and Mathematics
> Scholarship Program. His teaching and research interests are in engineeing mechanics, structural stability, engineering ethics, and engineering education. He is a recipient of the 2006 Ferdinand P. Beer and E. Russell Johnston, Jr. Outstanding New Mechanics Educator Award through the Mechanics Division of ASEE.

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Josh Bostwick Cornell University

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Josh Bostwick is a doctoral student in the Department of Theoretical and Applied Mechanics at Cornell University. He has B.S. degrees in Civil Engineering and Physics from the University of Wisconsin-Milwaukee. His research interests are in stability of interfacial fluid dynamics.

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Andrew Dressel University of Wisconsin-Milwaukee

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Andrew Dressel is a doctoral student in the Department of Civil Engineering and Mechanics at the University of Wisconsin-Milwaukee. He has a Master of Science degree in Mechanics from Cornell
University and a Bachelor of Science degree in Computer Science from Rensselaer Polytechnic Institute. His primary research interest is bicycle and motorcycle stability and handling.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Promoting Holistic Problem-Solving in Mechanics Pedagogy


The authors propose three strategies that are designed to enhance students’ understanding and problem-solving ability in introductory mechanics courses: (1) employing multiple- method problem-solving, in which students solve a given problem using more than one method; (2) organizing systems of linear equations into a standard “tabular” format which resembles matrix format; and (3) emphasizing the discussion and use of assumptions in problem-solving activities. The authors give a rationale for each strategy, present a review of several mechanics textbooks to determine the prevalence of these strategies, and provide local student performance data that, while as yet inconclusive, suggests a possible method for assessment of the strategies’ efficacy.


Mechanics provides the scientific foundation for nearly all branches of engineering and constitutes an essential component of the education of nearly all engineering students. Through mechanics, students learn not only fundamental principles that govern the behavior of structures and machines, but they also develop the rigorous habits of mind of establishing and critiquing assumptions, translating physical problems into well-posed mathematical equations, and assessing the meaning and validity of their solutions (possibly leading to reformulation and new solutions). It is this broader understanding of mechanics that informs our holistic approach to teaching.

In a previous work6 we studied the ability of mechanics students to think critically on the basis of their ability to use of free body diagrams, use vectors, coordinates and sign conventions, and address of units and physical dimension. We discovered that about three quarters of the time, students committed some error in at least one of these areas, even if they arrived at the correct answer. We also surveyed textbooks to determine how these matters are presented, and discovered several inconsistencies and inadequacies in their treatment.

Here we present three issues – referred to as the “targeted issues” – that we believe are important to promote problem-solving skills and broader understanding of mechanics. These issues are (1) multiple-method problem-solving, in which a given problem is solved in more than one way, (2) writing equations in a standard form that is amenable to computation, and (3) careful address of assumptions. Strategies to address these issues are referred to as the “targeted strategies”.

Considering the first issue, can material be developed in a general manner such that the choice of method is presented as a fundamental part of the problem-solving process? Or must certain problems be “pigeon-holed” such that their solutions are hard-wired to only a certain approach? We probe these questions using the example of solving problems with both polar coordinates and Cartesian coordinates.

Papadopoulos, C., & Bostwick, J., & Dressel, A. (2007, June), Promoting Holistic Problem Solving In Mechanics Pedagogy Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--3001

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